Koch snowflake

To continue drawing a Koch snowflake, trisect every line segment of the shape you have, and draw an equilateral triangle on the middle third of every line segment, pointing outward.

To continue drawing a Koch snowflake, trisect every line segment of the shape you have, and draw an equilateral triangle on the middle third of every line segment, pointing outward...

What you'd have, if you kept doing this for an infinite time, is a Koch snowflake. Since the Nth step requires that you draw 3(n-1) triangles, you're likely to get tired well before the heat death of the universe.

But try it for a few steps: first a triangle, then the next step you've drawn a Star of David, then you've drawn something with more points, and then you can see basically what a Koch snowflake looks like.

Take a straight line. Divide it into threeequal parts. Draw an equilateraltriangle using the central part as the base of the triangle. Erase the base of the triangle. You now have something which looks (roughly) like this: _/\_ Now do what you did to your original line to every straight line in the figure. Iterate.

In L-system and turtle graphics terms, this might be written as a system with {f,l,r} as the alphabet (interpreting `f' as forward, `l' as turning left 60 degrees, `r' as turning right 60 degrees), f -> flfrrflf as the only rule, and `frrfrrfrr' as the initial string.